{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:76A6IKPQO6U7KCOMQHEGMQUJGR","short_pith_number":"pith:76A6IKPQ","canonical_record":{"source":{"id":"1512.01702","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-12-05T21:03:26Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"adaf9bf29934835932f37449cabae3f33ba0d5999f2792ae177439c36607ff2d","abstract_canon_sha256":"ac7b22603f19bd161c091c9619e3de03a3ff86291a41c3dd71e285bc7eb2b27f"},"schema_version":"1.0"},"canonical_sha256":"ff81e429f077a9f509cc81c866428934635915c67e78cc9f6f6a4813b201e442","source":{"kind":"arxiv","id":"1512.01702","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.01702","created_at":"2026-05-18T00:48:01Z"},{"alias_kind":"arxiv_version","alias_value":"1512.01702v2","created_at":"2026-05-18T00:48:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.01702","created_at":"2026-05-18T00:48:01Z"},{"alias_kind":"pith_short_12","alias_value":"76A6IKPQO6U7","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"76A6IKPQO6U7KCOM","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"76A6IKPQ","created_at":"2026-05-18T12:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:76A6IKPQO6U7KCOMQHEGMQUJGR","target":"record","payload":{"canonical_record":{"source":{"id":"1512.01702","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-12-05T21:03:26Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"adaf9bf29934835932f37449cabae3f33ba0d5999f2792ae177439c36607ff2d","abstract_canon_sha256":"ac7b22603f19bd161c091c9619e3de03a3ff86291a41c3dd71e285bc7eb2b27f"},"schema_version":"1.0"},"canonical_sha256":"ff81e429f077a9f509cc81c866428934635915c67e78cc9f6f6a4813b201e442","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:01.386684Z","signature_b64":"aFfN/gVgRQRD9rI/NbcFA4PxMtqyJRp9IG6IbOL+tJjhDa0aGKmTIv+qztwtInB3GTrh2gmUFqZ9kHCoa2wZCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff81e429f077a9f509cc81c866428934635915c67e78cc9f6f6a4813b201e442","last_reissued_at":"2026-05-18T00:48:01.385975Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:01.385975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.01702","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:48:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BEZMpFfa+WGBvLUkYapCO5Jq5GzF8Gyq/CNPLy4W8UQ/hchon+KvFz6LpT6JeZFNy9t/G3rBADt9eONNiAyYCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T22:27:07.755781Z"},"content_sha256":"ae1631be7815e89fce2c734f995aa3e67e4ada699b2986058e035ce3fa039407","schema_version":"1.0","event_id":"sha256:ae1631be7815e89fce2c734f995aa3e67e4ada699b2986058e035ce3fa039407"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:76A6IKPQO6U7KCOMQHEGMQUJGR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Bohr sets of integer valued traceless matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"Alexander Fish","submitted_at":"2015-12-05T21:03:26Z","abstract_excerpt":"In this paper we show that any Bohr-zero non-periodic set $B$ of traceless integer valued matrices, denoted by $\\Lambda$, intersects non-trivially the conjugacy class of any matrix from $\\Lambda$. As a corollary, we obtain that the family of characteristic polynomials of $B$ contains all characteristic polynomials of matrices from $\\Lambda$. The main ingredient used in this paper is an equidistribution result for an $SL_d(\\mathbf{Z})$ random walk on a finite-dimensional torus deduced from Bourgain-Furman-Lindenstrauss-Mozes work."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.01702","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:48:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7Os+qFT4bGpT/OhlI/j6rWq5gFx7lnZ+F4JC+SSJivNDg4op0XZYSD6wYR8Qri8kXBOWaTYWKv/RuQVnmmqYBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T22:27:07.756118Z"},"content_sha256":"0a24966570cfef54448f280ddd8ebc215d31241e81bd2a60792894a90641f130","schema_version":"1.0","event_id":"sha256:0a24966570cfef54448f280ddd8ebc215d31241e81bd2a60792894a90641f130"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/76A6IKPQO6U7KCOMQHEGMQUJGR/bundle.json","state_url":"https://pith.science/pith/76A6IKPQO6U7KCOMQHEGMQUJGR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/76A6IKPQO6U7KCOMQHEGMQUJGR/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-01T22:27:07Z","links":{"resolver":"https://pith.science/pith/76A6IKPQO6U7KCOMQHEGMQUJGR","bundle":"https://pith.science/pith/76A6IKPQO6U7KCOMQHEGMQUJGR/bundle.json","state":"https://pith.science/pith/76A6IKPQO6U7KCOMQHEGMQUJGR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/76A6IKPQO6U7KCOMQHEGMQUJGR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:76A6IKPQO6U7KCOMQHEGMQUJGR","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"ac7b22603f19bd161c091c9619e3de03a3ff86291a41c3dd71e285bc7eb2b27f","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-12-05T21:03:26Z","title_canon_sha256":"adaf9bf29934835932f37449cabae3f33ba0d5999f2792ae177439c36607ff2d"},"schema_version":"1.0","source":{"id":"1512.01702","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.01702","created_at":"2026-05-18T00:48:01Z"},{"alias_kind":"arxiv_version","alias_value":"1512.01702v2","created_at":"2026-05-18T00:48:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.01702","created_at":"2026-05-18T00:48:01Z"},{"alias_kind":"pith_short_12","alias_value":"76A6IKPQO6U7","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"76A6IKPQO6U7KCOM","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"76A6IKPQ","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:0a24966570cfef54448f280ddd8ebc215d31241e81bd2a60792894a90641f130","target":"graph","created_at":"2026-05-18T00:48:01Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper we show that any Bohr-zero non-periodic set $B$ of traceless integer valued matrices, denoted by $\\Lambda$, intersects non-trivially the conjugacy class of any matrix from $\\Lambda$. As a corollary, we obtain that the family of characteristic polynomials of $B$ contains all characteristic polynomials of matrices from $\\Lambda$. The main ingredient used in this paper is an equidistribution result for an $SL_d(\\mathbf{Z})$ random walk on a finite-dimensional torus deduced from Bourgain-Furman-Lindenstrauss-Mozes work.","authors_text":"Alexander Fish","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-12-05T21:03:26Z","title":"On Bohr sets of integer valued traceless matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.01702","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ae1631be7815e89fce2c734f995aa3e67e4ada699b2986058e035ce3fa039407","target":"record","created_at":"2026-05-18T00:48:01Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"ac7b22603f19bd161c091c9619e3de03a3ff86291a41c3dd71e285bc7eb2b27f","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-12-05T21:03:26Z","title_canon_sha256":"adaf9bf29934835932f37449cabae3f33ba0d5999f2792ae177439c36607ff2d"},"schema_version":"1.0","source":{"id":"1512.01702","kind":"arxiv","version":2}},"canonical_sha256":"ff81e429f077a9f509cc81c866428934635915c67e78cc9f6f6a4813b201e442","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ff81e429f077a9f509cc81c866428934635915c67e78cc9f6f6a4813b201e442","first_computed_at":"2026-05-18T00:48:01.385975Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:01.385975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aFfN/gVgRQRD9rI/NbcFA4PxMtqyJRp9IG6IbOL+tJjhDa0aGKmTIv+qztwtInB3GTrh2gmUFqZ9kHCoa2wZCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:01.386684Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.01702","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae1631be7815e89fce2c734f995aa3e67e4ada699b2986058e035ce3fa039407","sha256:0a24966570cfef54448f280ddd8ebc215d31241e81bd2a60792894a90641f130"],"state_sha256":"4458561bfd350da2ae348c4e22697691bab84cc25bb970dd995d5f056f428ee8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8LgOJWx6EQIe/IQWltPShWAfG+sN07pwdM1TJjcW8GOXvl3EgZz/q7qSO7bZdXylvs+THloJY1YhpMOg2uKKAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T22:27:07.758118Z","bundle_sha256":"2f70b96be7d5b07387dfb3303840cb1bcd37071f3d62a280c91f35a654c9e278"}}